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The weird rules of quantum mechanics lead to all sorts of bizarre phenomena on tiny
scales— particles teleporting through walls or being in multiple places at
once or simultaneously existing and not. But wouldn't it be cool if we could see
some of this magical behavior on at a human scale. Well today I'm going to teach you how.
All you need is the second most abundant element in the universe and absolute cold.
Or if you don't have those, the corpse of a dead star will do just fine.
Perpetual motion machines are all scams. But perpetual motion itself is possible.
Sort of. If you stir a cup of tea you’ll create a vortex that slows down over time. But there is a
type of fluid in which the vortex will never stop—at least theoretically. Even unstirred,
it will climb the walls all by itself, and even leak through the microscopic channels
in the otherwise watertight porcelain. The fluid in question is liquid helium
cooled to near absolute zero when it becomes an exotic state of matter known as a superfluid.
Superfluidity is the most characteristic behavior of the bizarre state of matter called
the Bose-Einstein Condensate. This is a state of matter in which the weirdness of the quantum world
invades our large-scale reality. To understand this, we do need a bit of background—and that
background is our last episode where we talked about how the behavior of matter depends on how
nature counts its particles—described in the field of statistical mechanics. Watching that episode
either right now or right after this episode will really help your understanding of this phenomenon.
We’ll also be referring to this episode, but that you can definitely watch afterwards.
First though, let's recap just a little of what we learned in the last episode.
We saw that we can understand a lot of the behavior of matter by counting the number
of different ways in which particles can be divvied up into the available energy states.
Particles will tend to shuffle energy between each other until they have the most probable
energy distribution. The shape of that energy distribution determines the thermodynamics—which
means, how things like temperature, pressure, volume etc. relate to each other.
We also learned that there are different types of particles - bosons and fermions - which shuffle
around their energies differently. To remind you: no two fermions can occupy the same quantum state,
which means they can’t have exactly the same energies. On the other hand,
any number of bosons can occupy the same state. In everyday life, this difference doesn’t
matter. Everything else being equal, a cloud of bosons and a cloud of fermions behave the same.
But there are circumstances where the differences become very important. And
that includes the worlds of the very small—the quantum world. But also the world of the very
cold. There the quantum behaviors of these different particle types are as clear as day.
In our other previous episode we talked about the reason for the different behavior of bosons
and fermions—we saw how quantum spin determines the symmetry of the symmetry wavefunction,
and its this symmetry that determines whether two particles are allowed to have identical
wavefunctions. However that episode was on the mathy side, and also focused on fermions. For
now I want to try to give you a more intuitive view - and one that lets us understand the
behavior of bosons, which, afterall, is what we need to understand superfluids.
In quantum mechanics, we describe particles as wavefunctions—mathematical objects that encode
the probability that we will observe a certain position, velocity, whatever,
if we were to try to measure it. Wavefunctions are well named, because they’re wavy. For simplicity,
let’s just look at one component of a particle’s position wavefunction,
representing its blurry quantum location in space, which might look like this
wave-packet-a sine wave that tapers off on either side. The height of the wavefunction
at any point represents the probability of the particle actually being in that location.
Now let’s think about two particles moving together. At a certain point their wavefunctions
will overlap - and what happens then depends on the symmetry of the wavefunction. In this context,
when you have a symmetric wavefunction, then when they’re in the same quantum state their
peaks and valleys line up perfectly. A pair of symmetric wavefunctions can stack, doubling the
height of the peaks and the depth of the valleys. In the case of an anti-symmetric wavefunction,
if you try to put them in the same quantum state, the peaks of one will always valley line up with
the valleys of the other, and vice versa. In that case, overlapping the wavefunctions causes
the entire thing to cancel itself out, with the peaks of one negated by the valleys of the other.
The case of the symmetric wavefunction all of this is straightforward enough to
interpret. The fact that they can stack without canceling each other means that
particles of this type—bosons—can be placed in the same state without breaking any physics.
Fermions, on the other hand, with their antisymmetric wavefunctions, appear to cancel
each other out. If the wavefunction encodes their possible positions in space, then when they cancel
out there’s zero probability of either particle being anywhere. That doesn’t mean that pairs of
fermions destroys each other. That would break several conservation laws—from conservation of
energy, conservation of charge, even of quantum information. A wavefunction can’t just be deleted
from the universe. So rather than telling us that fermionic wavefunctions cancel each other out when
the overlap, this canceling effect actually tells us that fermions can’t ever overlap perfectly.
They can not ever occupy the same state. In fact if you try to push two of the same
type of fermion into the same state, they will resist with a force so powerful that, for example,
it can help a dead star resist collapsing into a black hole. But that’s another story.
This way of describing the difference between bosons and fermions is extremely heuristic—it’s
heavy on analogy and shouldn’t be interpreted too literally. For one thing, the part of the
wavefunction that’s symmetric or antisymmetric doesn’t look like a simple sine wave—it’s the part
of the wavefunction associated with the rotational state, not the position state. It’s connected to
particle spin. In fact, spin defines whether a wavefunction is symmetric or antisymmetric.
All particles with values of quantum spin that are an integer—so 0, 1, 2,
etc. are symmetric and are bosons. Those with half-integer spin—½, 3/2,
etc—and antisymmetric fermions. For a more nuanced description of all of this,
including a lot more on this spin stuff, check the episode I mentioned earlier.
But for now, let’s just take one critical fact from all of this:
bosons, with their integer spins and symmetric wavefunctions can be stacked,
fermions, with their half-integer spins and antisymmetric wavefunctions, cannot.
And by the way, all of the elementary matter particles—everything that makes up physical
stuff—are fermions. And the inability for them to perfectly overlap is why physical stuff
is physical in the first place—for example, atoms have structure because electrons can’t
all fall into the lowest atomic orbital together. On the other hand, photons and other bosons can
overlap completely and that's what makes lasers possible—a laser beam consists of many,
many photon wavefunctions that are perfectly overlapping, or in phase with each other.
So what would it look like if we could turn fe rmions into bosons? Would it be possible to make
an electron laser? Could we make atoms that collapse into super-dense states? Actually,
we can turn fermions into bosons, and one possible result is the Bose-Einstein condensate,
and this superfluid thing that I’ve been teasing at for the past several minutes.
Fermion wavefunctions have half-integer spin. Multiple fermion wavefunctions that
are somehow connected to each other have spins equal to the sum of those spins. For example,
a proton is made of three quarks, two with +½ and one with -½, adding those up you get a proton that
also has a spin of a ½ so is a fermion. But what if we could connect just two spin-½ particles?
That would give us a to spin of 1 which is an integer and so it should produce a boson.
Or take the helium-4 atom. It has two protons, two neutrons, and two electrons - all spin-½
particles. In this case, 3 are spin +½ and 3 spin -½, which gives the overall atom a
spin of 0. That’s an integer, therefore Helium-4 must be a boson. Its component particles remain
fermions and behave as fermions with respect to each other within the atom - they have
different internal energy states. But the entire helium-4 atom acts like a boson with respect to
its neighboring helium-4 atoms. That doesn’t mean they overlap in physical or position space—their
internal fermions would resist that. But the atoms as a whole can occupy identical energy states.
We really only see the effect of this at extremely low temperatures. So let’s do an experiment and
cool down some helium-4. At atmospheric pressure and room temperature the helium is a gas.
At this point it wouldn’t matter what the gas was—the shape of this distribution would look
the same and only depend on the temperature. But as temperature drops, more and more particles
move to lower energies. At around 5.2 K the gas condenses into a regular liquid.
But as we cool things down further, things start to look different.
If this was a gas of fermions, the inability of particles to occupy the same energy levels would
prevent all particles from falling to the lowest energy states. That has its own bizarre effects,
especially at very high pressures, but we’re talking about bosons here.
For the boson Helium-4 atoms, there’s nothing stopping all particles entering the lowest
energy state. When we hit a temperature of 2.17 K, close to absolute zero,
that’s exactly what happens. Rather than having a distribution of energies,
all particles have the same energy—the lowest possible energy. In fact they can’t have any
other energy because at this low temperature, there isn’t enough energy to jump to higher
states. But they also can’t lose energy - they already have the least possible energy.
In normal states of matter, when two atoms get close to each other they repel each other,
exchanging energy. Typically one loses energy and one gains it. But when all the particles
have the same energy then interactions that require the exchange of energy aren’t possible.
For example, a fluid made of such particles loses all friction. Normally, when fluids flow,
currents or streamlines within them that have different speeds within the fluid drag on each
other—we call that viscous drag. That drag is caused by particles at the streamline
boundaries colliding and exchanging energy, and it causes the flows to slow down. Such a
fluid has viscosity—the higher the viscosity, the more drag, and the less easily the fluid flows.
But the streamlines in very cold helium-4 don’t exchange energy with each other—they slide past
each other without friction, and so the fluid has zero viscosity. It is, in fact, a superfluid.
And now finally we get back to stirring our cup of tea. Particle interactions with
the walls and with each other cause the circular currents to slow down and stop.
But if your tea is superfluid helium-4, then these interactions can’t happen. Stir the cup
and the vortex should last forever. In reality, this would also require the walls of the cup to
be perfectly smooth. According to this cool simulation, when superfluid flows
around the microscopic bumps of a container wall it forms tiny perfectly-flowing vortices
that do actually slow down the overall flow, but in a different way to a regular fluid.
By the way, saying that all particles in a superfluid have the same energy is
a bit simplistic. Energy states can vary a bit across the fluid due to different
speeds of its streams, different heights in the gravitational field,
etc. But the point is that particles near each other are extremely close to having
the same energy state and so are restricted in how they can interact with each other.
There are a few other weird superfluid behaviors. All fluids will creep up
the walls of their containers a little bit due to the mild attraction between
the atoms of the fluid and container. But in a superfluid, the frictionlessness allows the
fluid to literally flow up the wall, at least once that wall is coated with enough fluid to itself be
frictionless. Then when the flow drops over the other side, it acts like a siphon, and can
drain your container of your precious helium-4. Superfluids will also flow through microscopic
fissures and pores in a container, causing it to appear to leak through apparently solid material.
This Houdini-like nature of helium-4 reminds me of quantum tunneling—how quantum objects can teleport
short distances through solid barriers. But this superfluid thing is NOT quantum tunneling,
however it is a true quantum effect, visible on a macroscopic scale. All of the behaviors
of superfluids are due to the quantized nature of the energy levels in the fluid.
Superfluids aren’t just a novelty found in physics labs. They are believed to exist for example
inside neutrons stars, where fermionic neutrons team up to act like bosons, and form these
whirlpools trom the surface of the star to its core that hold insane amounts of energy. They last
for a long time because-superfluid-but when they finally do break they are believed to cause the
neutron starquakes that we see in the glitches of pulsar signals. And superfluidity is basically
what electrons are doing inside the otherwise solid crystal lattices of a superconductor,
as we showed you in our episode on quasiparticles. In that case, the electrons connect with each
other over large distances to form Cooper pairs, so that these fermion pairs also act as bosons,
leading to frictionless flow of the electrons. This manifests as superconductivity.
At a more fundamental level, the fermionic quarks can join in pairs to become bosons, which allows
them to serve as strong-force-carrying mesons. The bosonic nature of the Higgs field allow its
particle to form a slightly different kind of condensate—one which fills the entire universe,
and which is responsible for giving elementary particles their mass. Now I feel like we’ve
pointed you to earlier episodes even more than we usual do in this episode. But, yeah, we have
one on the Higgs stuff also. But by now I think we’ve all realised that, just like with bosons,
there is no limit to the number of overlapping references to past episodes of Space Time.
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